Q. 79 - Precalculus Enhanced with Graphing Utilities

Question

If the graph of an equation is symmetric with respect to the origin and $-4$ is an $x$-intercept of this graph, name another $x$-intercept.

Step-by-Step Solution

Answer

The other $x$-intercept is $4$.

Step 1: Given information

The $x$-Intercept is $-4$, therefore the graph intersects the $x$-axis at $(-4,0)$.

Step 2: Determine the other point.

Since the graph is symmetric with respect to the origin, the following point is also on the graph:

$(-(-4),-0)$

Simplify the expression for the first coordinate by changing the sign of the number:

$(4,0)$

The graph intersects the $x$-axis at $(4,0)$ because the $y$-coordinate is $0$.

Step 3: Write the conclusion

Since the graph intersects the $x$-axis at $(4,0)$, the $x$-intercept occurs at $4$.